In the question, we are asked to find the discontinuity of the function below;
[tex]f(x)=\frac{x}{|x|}[/tex]Explanation
The discontinuity of a function is the point at which the function becomes undefined, or occurs at values of x where the graph can't be evaluated. This can be gotten by equating the denominator to zero and solving.
[tex]\mleft|x\mright|=0[/tex]Using the absolute rule
[tex]\mathrm{If}\: |u|\: =\: 0\: \mathrm{then}\: u\: =\: 0[/tex]Hence,
[tex]If\text{ }\mleft|x\mright|=0\text{ }\therefore\text{ }x=0[/tex]Answer
We can therefore conclude that the discontinuity occurs at x = 0
